Gregory died of heart failure on Saturday, his representative confirmed to The Hollywood Reporter.
"It is with enormous sadness that the Gregory family confirms that their father, comedic legend and civil rights activist Mr Dick Gregory departed this earth tonight in Washington, DC," his son Christian Gregory said via a statement from his father's representative.
"The family appreciates the outpouring of support and love and respectfully asks for their privacy as they grieve during this very difficult time."
Gregory was taken to the hospital earlier this month after feeling ill for a serious but stable medical condition, Christian added.
More From This Section
The St Louis native cynically satirised racism and other social ills during his routines.
Gregory's big break came in 1961 when he was booked into the Playboy Club in downtown Chicago as a one-night replacement for Irwin Corey, a white comic who didn't want to work seven nights a week.
He was invited to perform on "The Tonight Show" in 1962.
Gregory used his newfound fame to become a civil-rights activist and opponent of the Vietnam War.
Gregory ran for mayor of Chicago in 1967 but lost to Richard Daley, then entered the race for US president a year later.
A write-in candidate on the Peace and Freedom Party ticket, he received some 47,000 votes.
In 2016, Emmy-winning actor Joe Morton portrayed Gregory in the off-Broadway play "Turn Me Loose", produced by John Legend.